Calculating Capacity – “Making Jello Feel Like Concrete”

December 21st, 2010 3:43 pm Category: Optimization, Scheduling, by: John Hughes

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Frequently, you might hear somebody say that the capacity of a production facility is some known and fixed value.  When this happens be very wary of what they might be trying to sell you.  Because as with so many other things, when measuring capacity “the devil is in the details”.

The “capacity” of a factory sounds like a pretty simple notion and something that should be easy to calculate.  But this is only true for production systems that are fairly straightforward, consisting of totally independent machines and processes.  If the organization however consists of operations that are interconnected and interdependent on each other, then capacity can be a fairly difficult thing to measure.

In the vast majority of production systems, there is a very real link between capacity and three critical factors:

  1. the mix of products, and how much time is required for setup/cleanup between consecutive production runs,
  2. the ability to create sophisticated and optimal schedules for the production resources,
  3. how much physical space exists in the factory where products that are only partially complete can be kept or stored; what’s known as Work in Process (or WIP)  Inventory.

To see these 3 relationships at work, consider the simple case where a certain department produces two products, A and B, which both use the same piece of equipment, and there is only one of these machines available.  The production rates of the machine are in the table below and there is a 4 hour setup time required when the machine switches over from producing one product to another.  Now consider the 2 scenarios below.  In Scenario A, the capacity is 170 units per day while in scenario B the capacity is 145.

    Scenario A   Scenario B
  ProductionRate (Units / hr) Daily Sched Qt. Hrs required   Daily Sched Qt. Hrs required
A 12 100 8.33   50 4.17
B 6 70 11.67   95 15.83
Tot   170 20   145 20
  Setup hrs ->   4     4
  Grand Total   24     24

This example clearly demonstrates the frist item above, that the “capacity” of the department depends to a large extent on the mix of the 2 products that are being produced.

Now suppose that management wants to produce 110 of A and 80 of B per day.  These new requirements seem to clearly exceed the capacity of the department given EITHER Scenario A or B.  But maybe the necessary capacity can still be found.

If the new requirement is to produce at this increased rate for only a single day, or to produce at this rate each and every day, then there is definitely not enough capacity on the machine.  However, if the increased production is required over a sustained length of time, then we can gain extra production by modifying the production schedule so as to eliminate or minimize the occurrence of the 4 hour setup.  If the department schedules production in long blocks spanning several days, where first one product and then the other is produced, then the department DOES have the capacity.  In the table below for example, 440 units of A is first produced followed by 320 of B, with a 4 hour setup between them.  This represents 4 days worth of the increased management requirement (100 of A and 80 of B each multiplied by 4).

  ProductionRate (Units / hr) Sched Qt. Hrs required
A 12 440 36.67
B 6 320 53.33
Tot   760 90
  Setup hrs ->   4
  Grand Total   94

With this schedule, the total required hours of 94 is less than the 96 hours available in 4 days, and so now there IS enough capacity!  By scheduling wisely (i.e. “working smarter”), the department’s average daily capacity has actually risen to (760 / 4) = 190 units per day, a good deal higher than either 170 or 145 in the two previous scenarios.

Thus, the department capacity clearly depends on the ability to implement “smart” production schedules that make the best use of the available resources, i.e. the second issue mentioned earlier.

Finally, this higer capacity schedule is an example of a “good news / bad news” situation.  Although the plant is able to produce more (and presumably company revenues will go up) the downside of this higher capacity schedule is that  the department will be maintaining a larger amount of inventory in the supply chain on average.  And if there is more “stuff” in the pipeline, then there has to be the physical space to put it.  This is an important consideration if inventory has to be stored in or on particular types of storage facilities such as refrigerators or special racks.  Therefore, although it might be possible to “buy” extra production capacity with a better equipment schedule,  it is important to realize that different schedules put more or less demand on the spatial capacity of the actual storage facilities.

Therefore, this example illustrates the third item, that increasing ouput can put stress on the plant’s storage facilities

This last scenario also shows that maximum capacity is not necessarily the same as minimum cost.  Because notice that in this scenario there is only one 4-hour setup, and thus any costs from the setup activity are averaged over a larger number of produced items.  But offsetting this savings in setup cost is the fact that with the increased WIP, the inventory costs will have gone up.

The fact that capacity can be such a difficult thing to measure, does not mean that it is not a valuable parameter to describe a given system.  What it does mean is that when any capacity value is given for a particular supply chain, it is absolutely critical to understand the assumptions that underlie it.  The fact that capacity is such a highly maleable concept, simply reinforces the fact that managing a company’s supply chain is always a delicate balancing act between competing costs and non-monetary factors.

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